Study On The Problems And Counter Measures Of Sixth Graders' Understanding Of Fractional Concept Based On APOS Theory

Mathematics concept is a huge system,the understanding of the concept of fraction is a very important part of mathematics learning.Because of the rich connotation of the concept of fraction,and has a certain abstraction,the primary school students are easy to understand the concept of fraction is not in place and there are problems.Based on APOS theory,this study emphasizes the establishment of appropriate mental structure in stages to help students understand the concept of fractions.This research takes literature analysis,questionnaire survey and interview as the main survey methods.According to APOS theory,we designed the student test paper and the teacher questionnaire respectively,and investigated 260 sixth grade students and 30 primary school math teachers in a primary school in Jinzhou.At the same time,representative students with test results are also interviewed as a supplement to the survey of test papers.The results show that the sixth graders' understanding level of fractional concepts decreases with the increase of conceptual difficulty.The sixth grade students' understanding of the five sub-concepts of fractions is different.The problems existing in the sixth grade students' understanding of the five subconcepts can be summarized as follows: the understanding of the concept of fraction in the operation stage is relatively simple;The process stage cannot accurately summarize the nature of the concept of fraction;In the object stage,the concept of fractions is not clear enough.Schema stage can not build the relationship between concepts well.Based on the attribution analysis of the existing problems,the strategies with high applicability are put forward,which are: the operation stage,the creation of activity situation;Process stage,reflecting on operational activities;Object stage,concept consolidation and application;Schema stage,conceptual system connection.It is hoped that this research can help the sixth graders to understand the concept of fraction better to some extent,and provide reference for improving the teaching quality of the concept of fraction according to the teaching strategies proposed by the research.